Albert Barnes on Acts 13:12

Then the deputy--believed. Was convinced that Elymas was an impostor, and that the doctrine of Paul was true. There seems no reason to doubt that his faith was that which is connected with eternal life; and if so, it is an evidence that the gospel was not always confined to the poor, and to the obscure ranks of life.

At the doctrine of the Lord. The word doctrine here seems to denote, not the teaching or instruction, but the wonderful effects which were connected with the doctrine. It was particularly the miracle with which he was astonished; but he might have been also deeply impressed and amazed at the purity and sublimity of the truths which were now expanded to his view. We learn nothing further respecting him in the New Testament.